Eric C. answered • 12/10/15

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Hey Keiana.

This is a simple plug 'n chug question from the simple interest formula.

A = P(1 + r/n)^nt

A = amount after time t

P = principal invested

r = interest rate

n = how many times a year its compounded

t = time

In your case:

A = 2*6000

P = 6000

r = 5.5% = 0.055

n = 12, since there are 12 months per year

t = ???

2*6000 = 6000(1 + 0.055/12)^12t

2 = (1 + 0.055/12)^12t

Take the natural log of both sides to bring the 12t down from the exponent.

ln(2) = ln(1 + 0.055/12)^12t

ln(2) = 12t*ln(1 + 0.055/12)

Solve for t.

ln(2)/ ln(1 + 0.055/12) = 12t

t = ln(2) / (12*ln(1 + 0.055/12))

t = 12.63 years

Hope this helps.

Eric C.

12/10/15